Improving interim decisions in randomized trials by exploiting information on short‐term endpoints and prognostic baseline covariates

Abstract

Conditional power calculations are frequently used to guide the decision whether or not to stop a trial for futility or to modify planned sample size. These ignore the information in short-term endpoints and baseline covariates, and thereby do not make fully efficient use of the information in the data. We therefore propose an interim decision procedure based on the conditional power approach which exploits the information contained in baseline covariates and short-term outcomes. We will realise this by considering the estimation of the treatment effect at the interim analysis as a missing data problem. This problem is addressed by employing specific prediction models for the long-term endpoint which enable the incorporation of baseline covariates and multiple short-term endpoints. We show that the proposed procedure leads to an efficiency gain and a reduced sample size, without compromising the Type I error rate of the procedure, even when the adopted prediction models are misspecified. In particular, implementing our proposal in the conditional power approach allows earlier decisions relative to standard approaches, whilst controlling the probability of an incorrect decision. This time gain results in a lower expected number of recruited patients in case of stopping for futility, such that fewer patients receive the futile regimen. We explain how these methods can be used in adaptive designs with unblinded sample size reassessment based on the inverse normal p-value combination method to control type I error. We support the proposal by Monte Carlo simulations based on data from a real clinical trial.

Clinical Trials Impacted by the COVID-19 Pandemic: Adaptive Designs to the Rescue?

“…If primary endpoint data are available, another approach is to retain the prespecified long-term endpoint as the primary focus of the interim analysis, but to support it with information on short-term data. In particular, such methodology exploits the possible statistical association between the short- and long-term endpoints to provide information about the long-term primary endpoint on patients who did not reach their primary endpoint yet (e.g., Galbraith and Marschner 2003 ; Sooriyarachchi et al 2006 ; Stallard 2010 ; Niewczas, Kunz, and König 2019 ; Van Lancker, Vandebosch, and Vansteelandt 2020 ). To maintain the Type I error—even if all unblinded available first-stage data are used in the adaptation decisions, it is recommended to define the first stage p -value by the cohort of patients included before the interim analysis (e.g., Jenkins, Stone, and Jennison 2011 ).…”

“…To maintain the Type I error—even if all unblinded available first-stage data are used in the adaptation decisions, it is recommended to define the first stage p -value by the cohort of patients included before the interim analysis (e.g., Jenkins, Stone, and Jennison 2011 ). In comparison with the other existing methods for binary and continuous endpoints, the method of Van Lancker, Vandebosch, and Vansteelandt ( 2020 ) has the advantage of making fully efficient use of the information in the data by, besides multiple short-term endpoints, also taking into account baseline measurements.…”

“…As long as the estimand of interest is the (hypothetical) treatment effect not impacted by COVID-19, these analyses will be unbiased if only pre-COVID-19 data are used. For example, in the situation where the number of patients before the COVID-19 impact may already be sufficient to provide reasonable power (see Section 4.1), the use of short-term information to estimate primary endpoint might lead to an even higher power (e.g., Van Lancker, Vandebosch, and Vansteelandt 2020 ). In situations where it is not feasible to obtain sufficient information from the pre-COVID-19 patients, it may be advisable to support the interim analysis with historical data (Van Lancker et al 2019 ).…”

“…However, in studies where the estimand of interest is defined with respect to the combination of pre-, during-, and post-COVID-19 patients, predicting the long-term primary endpoint of patients who are still at risk to be impacted by COVID-19 with prediction models based on pre-COVID-19 data only, will lead to biased estimators. Although the prediction models used in Van Lancker, Vandebosch, and Vansteelandt ( 2020 ) could be adapted to account for the (expected) dilution effect, this would require strong assumptions about the effect of the longitudinal measurements on the dilution; which falls out of the scope of this article. We therefore recommend using the methods presented in Section 4 to modify the trial.…”

“…Note that the different methods described in this section can also take into account missing data (e.g., due to COVID-19-related drop-out) if one can assume that the missing mechanism is missing completely at random. In the appendix of Van Lancker, Vandebosch, and Vansteelandt ( 2020 ), an extension of their method that allows the weaker assumption that missingness is at random is discussed. An alternative for the other methods is to consider more detailed informative missingness models (e.g., via multiple imputation (Sterne et al 2009 )).…”